# Carbon-14 has a half-life of 5,730 years. How long will it take for 112.5 g of a 120.0 g sample to decay radioactively?

Aug 9, 2016

$22920$ years

#### Explanation:

The half life of a substance is the time taken for the amount of a substance present to halve. If 112.5g has decayed we have 7.5g left. To get to 7.5g we need to halve 120g four times.

$120 \rightarrow 60 \rightarrow 30 \rightarrow 15 \rightarrow 7.5$

The total time elapsed in this time will be four times the half life, so

$T = 4 \cdot {t}_{\frac{1}{2}} = 4 \cdot 5730 = 22920$ years